Introduction: Study Details & Relevant Background Information

Introduction: Areas of Particular Interest

Data and Analysis

  • We want to investigate the overall association between social deficits and motor skills for each diagnosis group.

    > Primary Endpoint: What motor skills are associated with SRS scores for each diagnosis group.

    > Secondary Endpoint: What factors influence this association?

  • Data Collected for Investigation and Analysis:
    • Age
    • Handedness (quantified by Edinburgh Handedness Integer)
    • Gender
    • Primary and Secondary Diagnosis
    • SRS Total
    • mABC Total and Subscores
    • WISC Score

Methods: Cleaning Data

Primary Count Avg Age Males Females RightHanded LeftHanded
ASD 138 10.236 116 22 124 20
ADHD 176 9.6908 124 52 285 36
TD 254 10.2146 185 69 307 42

Methods: Exploring Motor Skills

Methods: Other Variables

Proposed Models

\[ \text{E[Social Deficit Score]} = \textbf{X} * \boldsymbol{\beta} \\ where: \\ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} \]

\[ H_0: \text{Mean of SRS Total Scores from Version 1 = Mean of SRS Total Scores from Version 2} \\ H_1: \text{Mean of SRS Total Scores from Version 1} \space \neq \text{Mean of SRS Total Scores from Version 2} \\ \text{Under the null we got a t-statistc of -6.03 from a t-distribution of 417.38 Degrees of Freedom} \\ \text{that has a p-value of} \space 3.511 \times 10^{-9} \\ \space \text{Under} \space \alpha = .05 \space \text{we reject the null} \text{ and believe that there is a true difference in the mean} \]

Resutls: Typically Developing

## 
## Call:
## lm(formula = SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore + 
##     mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer + 
##     GAI + Gender + mABC_AGE, data = nodia2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9465 -2.7041 -0.5293  1.5000 18.0316 
## 
## Coefficients:
##                                                Estimate Std. Error t value
## (Intercept)                                    43.52523    4.62720   9.406
## mABC_AimingAndCatching.Component.StandardScore  0.01693    0.19383   0.087
## mABC_Balance.Component.StandardScore           -0.14406    0.16893  -0.853
## EdinburghHandedness_Integer                    -1.46571    1.07791  -1.360
## GAI                                             0.05956    0.03199   1.862
## GenderM                                        -1.12175    1.24382  -0.902
## mABC_AGE                                       -0.09471    0.42545  -0.223
##                                                Pr(>|t|)    
## (Intercept)                                    1.55e-15 ***
## mABC_AimingAndCatching.Component.StandardScore   0.9306    
## mABC_Balance.Component.StandardScore             0.3958    
## EdinburghHandedness_Integer                      0.1769    
## GAI                                              0.0655 .  
## GenderM                                          0.3692    
## mABC_AGE                                         0.8243    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.727 on 103 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.06594,    Adjusted R-squared:  0.01153 
## F-statistic: 1.212 on 6 and 103 DF,  p-value: 0.3062

Results: ADHD

\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{ADHD Subtype Inattentive} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 64.0176 \\ -2.3512 \\ 1.3089 \\ 8.3848 \\ 0.0620 \\ -13.9720 \\ -9.3211 \\ -1.1236 \end{bmatrix} \]

## Analysis of Variance Table
## 
## Model 1: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore + 
##     mABC_Balance.Component.StandardScore
## Model 2: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore + 
##     mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer + 
##     GAI + ADHD_Subtype + Gender + mABC_AGE
##   Res.Df   RSS Df Sum of Sq      F   Pr(>F)   
## 1     90 32488                                
## 2     85 25962  5    6526.4 4.2735 0.001626 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[ H_0: \text{Just Balance and Catching is Sufficient} \\ H_1: \text{Full Model is Sufficient} \\ \text{Under the null we got an F-statistic of 4.2735 where} \ F \sim F_{5,85} \\ \text{which gives us a p-value of .0016 with an} \ \alpha = .05 \ \text{we reject the null} \\ \text{and believe that we should keep every coefficient in the full model} \]

\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{ADHD Subtype Inattentive} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 54.637 \\ 0.2525 \\ -0.9143 \\ 0.4960 \\ 0.0037 \\ -8.7537 \\ 1.6450 \\ 0.5879 \end{bmatrix} \]

## Analysis of Variance Table
## 
## Model 1: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore + 
##     mABC_Balance.Component.StandardScore
## Model 2: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore + 
##     mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer + 
##     GAI + ADHD_Subtype + Gender + mABC_AGE
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     77 4764.4                              
## 2     72 4027.4  5    736.99 2.6351 0.03034 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[ H_0: \text{Just Balance and Catching is Sufficient} \\ H_1: \text{Full Model is Sufficient} \\ \text{Under the null we got an F-statistic of 2.6351 where} \ F \sim F_{5,72} \\ \text{which gives us a p-value of .03 with an} \ \alpha = .05 \ \text{we reject the null} \\ \text{and believe that we should keep every coefficient in the full model} \]

Results: ASD

\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Secondary Diagnosis Yes} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 89.60022 \\ 0.47326 \\ -2.28800 \\ 13.96288 \\ -0.01026 \\ 1.25663 \\ 0.45815 \\ 0.87001 \end{bmatrix} \]

\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Secondary Diagnosis Yes} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 58.690482 \\ 0.179097 \\ 0.767967 \\ -2.043116 \\ 0.113743 \\ 8.627154 \\ -4.782354 \\ 0.002163 \end{bmatrix} \]